It has been known that, in the production of propylene oxide from propylene, oxygen, and hydrogen with use of a noble metal catalyst and a crystalline titanosilicate catalyst, the use of a palladium catalyst and a TS-I catalyst in combination with a phosphorus modifier, a sulfur modifier or the like reduces an amount of a propane byproduct (See, for example, Japanese Translation of PCT International Application, No. 511454/2002 (Tokuhyou 2002-51 1454), which is an equivalent of WO99/52884). The addition of a phosphorus modifier, however, involves use of an organic phosphorus compound, which has a negative influence on the environment. Further, there is another disadvantage in that the addition of a sulfur modifier reduces the production amount of propylene oxide. Another known method for producing propylene oxide involves use of palladium and a Ti-MWW catalyst in combination with water and acetonitrile as a solvent (See Heisei 14 nendo Jisedai Kagaku Process Gijutu Kaihatu Non-halogen Kagaku Process Gijutu Kaihatu Seiko Houkokusho (Report of R&D projects for Technology of Next-generation Chemical Process/Technology for Non-halogen Chemical Process, FY2002 Annual Report), pp. 152-180,(2003)).). Unfortunately, the above methods for producing propylene oxide are not sufficiently efficient.